The present invention relates to methods of designing ophthalmic lenses that provide the eye with reduced aberrations, as well as lenses capable of providing such visual improvements.
It is presently discussed that the visual quality of eyes having an implanted intraocular lens (IOL) is comparable with normal eyes in a population of the same age. Consequently, a 70 year old cataract patient can only expect to obtain the visual quality of a non-cataracteous person of the same age after surgical implantation of an intraocular lens, although such lenses objectively has been regarded as optically superior than the natural crystalline lens. This result is likely to be explained by the fact that present IOLs are not adapted to compensate for defects of the optical system of the human eye. Age-related defects of the eye have recently been investigated and it is found that contrast sensitivity significantly declines in subjects older than 50 years. These results seem to comply with the above-mentioned discussion, since the contrast sensitivity measurements indicate that individuals having undergone cataract surgery with lens implantation lens will not obtain a better contrast sensitivity than persons of an average age of about 60 to 70 years.
Even if intraocular lenses aimed to substitute the defect cataract lens and other ophthalmic lenses, such as conventional contact lenses, have been developed with excellent optical quality, it is obvious that they fail to correct for a number of aberration phenomena of the eye including age-related aberration defects.
U.S. Pat. No. 5,777,719 (Williams et. al.) discloses a method and an apparatus for accurately measuring higher aberrations of the eye as an optical system with wavefront analysis. By using a Hartmann-Shack wavefront sensor, it is possible to measure higher order aberrations of the eye and using such data to find compensation for these aberrations and thereby obtain sufficient information for the production of an optical lens, which can provide a highly improved optical correction. The Hartmann-Shack sensor provides means for obtaining light reflected from the retina of the eye of a subject. The wavefront in the plane of the pupil is recreated in the plane of the lenslet array of the Hartmann-Shack sensor. Each lenslet in the array is used to form an aerial image of the retinal point source on a CCD camera located adjacent to the array. The wave these aberrations and thereby obtain sufficient information for the design of an optical lens, which can provide a highly improved optical performance. The Hartmann-Shack sensor provides means for analyzing light reflected from a point on the retina of the eye of a subject. The wavefront in the plane of the pupil is recreated in the plane of the lenslet array of the Hartmann-Shack sensor. Each lenslet in the array is used to form an aerial image of the retinal point source on a CCD camera located at the focal plane of the array. The wave aberration of the eye, in the form resulting from a point source produced on the retina by a laser beam, displaces each spot by an amount proportional to the local slope of the wavefront at each of the lenslets. The output from the CCD camera is sent to a computer, which then performs calculations to fit slope data to the first derivatives of 66 Zernike polynomials. From these calculations, coefficients for weighting the Zernike polynomials are obtained. The sum of the weighted Zernike polynomials represents a reconstructed wavefront distorted by the aberrations of the eye as an optical system. The individual Zernike polynomial terms will then represent different modes of aberration.
U.S. Pat. No. 5,050,981 (Roffman) discloses-another method for designing a lens by calculating modulation transfer functions from tracing a large number of rays through the lens-eye system and evaluating the distribution density of the rays in the image position. This is repeatedly performed by varying at least one lens surface until a lens is found which results in a sharp focus and a maximum modulation transfer function.
U.S. Pat. No. 6,224,211 (Gordon) describes a method of improving the visual acuity of the human eye by successively fitting aspheric lenses to the cornea and thereby finding a lens that can reduce spherical aberration of the whole individual eye.
The methods referred to above for designing are suitable for the design of contact lenses or other correction lenses for the phakic eye which can be perfected to compensate for the aberration of the whole eye system. However, to provide improved intraocular lenses aimed to replace the natural crystalline lens, it would be necessary to consider the aberrations of the individual parts of the eye.
U.S. Pat. No. 6,050,687 (Bille et al) refers to a method wherein the refractive properties of the eye are measured and wherein consideration is taken to the contribution of the individual surfaces of the eye to the total wavefront aberrations. The method described herein particularly aims at analyzing the topography of the posterior corneal surface in order to improve refractive correction techniques.
There has recently been a focus on studying the aberrations of the eye, including a number of studies of the development of these aberrations as a function of age. In two particular studies, the development of the components of the eye were examined separately, leading to the conclusion that the optical aberrations of the individual components of younger eyes cancel each other out, see Optical Letters, 1998, Vol. 23(21), pp. 1713-1715 and IOVS, 2000, Vol 41(4), 545. The article of S. Patel et al in Refractive and Corneal Surgery, 1993, Vol. 9, pages 173-181 discloses the asphericity of posterior corneal surfaces. It is suggested that the corneal data can be used together with other ocular parameters to predict the power and the asphericity of an intraocular lens with the purpose of maximizing the optical performances of the future pseudophakic eye. Furthermore, it was also recently observed by Antonio Guirao and Pablo Artal in IOVS, 1999, Vol. 40(4), S535 that the shape of the cornea in the subjects provides a positive spherical. These studies indicate that the cornea in the subjects provides a positive spherical aberration, which increases slightly with the age. On the other hand, the rotationally symmetric aberration of the anterior corneal surface does not seem to be different between younger and older eye according to results found by T Oshika et al in Investigative Ophthalmology and Visual Science, 1999, Vol 40, pp. 1351-1355. In Vision Research, 1998, 38(2), pp. 209-229, A Glasser et al. investigated the spherical aberration of natural crystalline lenses from eyes obtained from an eye bank after the cornea has been removed. According to the laser scanner optical method used herein it was found that the spherical aberration from an older lens (66 years) shows positive spherical aberration, whereas a 10-year-old lens shows negative spherical aberration. In addition, Vision Research, 2001, 41, pp.235-243 (G Smith et al) discloses that the natural crystalline lens appears to have negative spherical aberration when in the relaxed state. Smith et al suggest that because older eyes have a larger aberration, it is likely that the spherical aberration of the crystalline lens becomes less negative with age.
In Ophthal. Physiol. Opt., 1991, Vol. 11, pp. 137-143 (D A Atchison) it is discussed how to reduce spherical aberrations in intraocular lenses by aspherizing the lens surface. The methods outlined by Atchison are based on geometric transferring calculations, which do not consider diffraction effects and any variations in refractive index along the ray path in inhomogeneous elements. These calculations will lead to errors close to the diffraction limit. Also in WO 98/31299 (Technomed) a ray tracing method is outlined according to which the refraction of the cornea is attempted to be considered for the design of an intraocular lens. In view of the foregoing, it is apparent that there is a need for ophthalmic lenses that are better adapted or compensated to the aberrations of the individual surfaces of the eye and are capable of better correcting aberrations other than defocus and astigmatism, as provided by conventional ophthalmic lenses.
It is an object of the invention to provide for methods that result in obtaining an ophthalmic lens, which provides the eye with reduced aberrations.
It is another object of the invention to provide methods of obtaining an intraocular lens capable of reducing the aberration of the eye after its implantation into the eye.
It is a further object to provide for methods of obtaining an intraocular lens capable of compensating the aberrations resulting from optical irregularities in the corneal surfaces.
It is a still further object of the present invention to provide an intraocular lens which is capable of restoring a wavefront deviating from sphericity into a substantially more spherical wavefront.
It is also an object of the present invention to provide an intraocular lens which is capable of correcting for mean optical irregularities and imperfections found in a particular group of people and thereby provide a lens with improved optical performance for an individual belonging to the same group.
The present invention generally relates to an ophthalmic lens and to methods of obtaining said ophthalmic lens that is capable of reducing the aberrations of the eye. By aberrations in this context is meant wavefront aberrations. This is based on the understanding that a converging wavefront must be perfectly spherical to form a point image, i.e. if a perfect image shall be formed on the retina of the eye, the wavefront having passed the optical surfaces of the eye, such as the cornea and a natural or artificial lens, must be perfectly spherical. An aberrated image will be formed if the wavefront deviates from being spherical. In this context the term nonspherical surface will refer to rotationally symmetric, asymmetric and/or irregular surfaces, i.e. all surfaces differing from a sphere. The wavefront aberrations can be expressed in mathematical terms in accordance with different approximate models as is explained in textbook references, such as M. R. Freeman, Optics, Tenth Edition, 1990.
In a first embodiment, the present invention is directed to a method of designing an intraocular lens capable of reducing aberrations of the eye after its implantation. The method comprises a first step of characterizing at least one corneal surface as a mathematical model and by employing the mathematical model calculating the resulting aberrations of the corneal surface. An expression of the corneal aberrations is thereby obtained, i.e. the wavefront aberrations of a spherical wavefront having passed such a corneal surface. Dependent on the selected mathematical model different routes to calculate the corneal aberrations can be taken. Preferably, the corneal surface is characterized as a mathematical model in terms of a conoid of rotation or in terms of polynomials or a combination thereof. More preferably, the corneal surface is characterized in terms of a linear combination of polynomials. The second step of the method is to select the power of the intraocular lens, which is done according to conventional methods for the specific need of optical correction of the eye, for example the method described in U.S. Pat. No. 5,968,095. From the information of steps one and two an intraocular lens is modeled, such that a wavefront from an optical system comprising said lens and corneal model obtains reduced aberrations. The optical system considered when modeling the lens typically includes the cornea and said lens, but in the specific case it can also include other optical elements including the lenses of spectacles, or an artificial correction lens, such as a contact lens, a corneal inlay implant or an implantable correction lens depending on the individual situation.
Modeling the lens involves selection of one or several lens parameters in a system which contributes to determine the lens shape of a given, pre-selected refractive power. This typically involves the selection of the anterior radius and surface shape, posterior radius and surface shape, the lens thickness and the refractive index of the lens. In practical terms, the lens modeling can be performed with data based on a conventional spherical lens, such as the CeeOn(copyright) lenses from Pharmacia Corp., as exemplified with the CeeOn(copyright) Edge (Model 911). In such a case, it is preferred to deviate as little as possible from an already clinically approved model. For this reason, it may be preferred to maintain pre-determined values of the central radii of the lens, its thickness and refractive index, while selecting a different shape of the anterior and/or posterior surface, thus providing one or both of these surfaces to have an nonspherical shape. According to an alternative of the inventive method, the spherical anterior surface of the conventional starting lens is modeled by selecting a suitable aspheric component. Preferably the lens has at least one surface described as a nonsphere or other conoid of rotation. Designing nonspherical surfaces of lenses is a well-known technique and can be performed according to different principles and the description of such surfaces is explained in more detail in our parallel Swedish Patent Application 0000611-4 to which is given reference.
The inventive method can be further developed by comparing wavefront aberrations of an optical system comprising the lens and the model of the average cornea with the wavefront aberrations of the average cornea and evaluating if a sufficient reduction in wavefront aberrations is obtained. Suitable variable parameters are found among the above-mentioned physical parameters of the lens, which can be altered so as to find a lens model, which deviates sufficiently from being a spherical lens to compensate for the corneal aberrations.
The characterization of at least one corneal surface as a mathematical model and thereby establishing a corneal model expressing the corneal wavefront aberrations is preferably performed by direct corneal surface measurements according to well-known topographical measurement methods which serve to express the surface irregularities of the cornea in a quantifiable model that can be used with the inventive method. Corneal measurements for this purpose can be performed by the ORBSCAN(copyright) videokeratograph, as available from Orbtech, or by corneal topography methods, such as EyeSys(copyright) from Premier Laser Systems. Preferably, at least the front corneal surface is measured and more preferably both front and rear corneal surfaces are measured and characterized and expressed together in resulting wavefront aberration terms, such as a linear combination of polynomials which represent the total corneal wavefront aberrations. According to one import aspect of the present invention, characterization of corneas is conducted on a selected population with the purpose of expressing an average of corneal wavefront aberrations and designing a lens from such averaged aberrations. Average corneal wavefront aberration terms of the population can then be calculated, for example as an average linear combination of polynomials and used in the lens design method. This aspect includes selecting different relevant populations, for example in age groups, to generate suitable average corneal surfaces. Advantageously, lenses can thereby be provided which are adapted to an average cornea of a population relevant for an individual elected to undergo cataract surgery or refractive correction surgery including implantation of an IOL or corneal inlays. The patient will thereby obtain a lens that gives the eye substantially less aberrations when compared to a conventional spherical lens.
Preferably, the mentioned corneal measurements also include the measurement of the corneal refractive power. The power of the cornea and the axial eye length are typically considered for the selection of the lens power in the inventive design method.
Also preferably, the wavefront aberrations herein are expressed as a linear combination of polynomials and the optical system comprising the corneal model and modeled intraocular lens provides for a wavefront having obtained a substantial reduction in aberrations, as expressed by one or more such polynomial terms. In the art of optics, several types of polynomials are available to skilled persons for describing aberrations. Suitably, the polynomials are Seidel or Zernike polynomials. According to the present invention Zernike polynomials preferably are employed.
The technique of employing Zernike terms to describe wavefront aberrations originating from optical surfaces deviating from being perfectly spherical is a state of the art technique and can be employed for example with a Hartmann-Shack sensor as outlined in J. Opt. Soc. Am., 1994, Vol. 11(7), pp. 1949-57. It is also well established among optical practitioners that the different Zernike terms signify different aberration phenomena including defocus, astigmatism, coma and spherical aberration up to higher aberrations. In an embodiment of the present method, the corneal surface measurement results in that a corneal surface is expressed as a linear combination of the first 15 Zernike polynomials. Be means of a ray tracing method, the Zernike description can be transformed to a resulting wavefront (as described in Equation (1)), wherein Z1 is the i-th Zernike term and ai is the weighting coefficient for this term. Zernike polynomials are a set of complete orthogonal polynomials defined on a unit circle. Below, Table 1 shows the first 15 Zernike terms and the aberrations each term signifies.                               z          ⁡                      (                          ρ              ,              θ                        )                          =                              ∑                          i              ⁢                              xe2x80x83                            ⁢              …              ⁢                              xe2x80x83                            ⁢              1                        15                    ⁢                                    α              i                        ⁢                          xe2x80x83                        ⁢                          Z              i                                                          (        1        )            
In equation (1), xcfx81 and xcex8 represent the normalized radius and the azimuth angle, respectively.
Conventional optical correction with intraocular lenses will only comply with the fourth term of an optical system comprising the eye with an implanted lens. Glasses, contact lenses and some special intra ocular lenses provided with correction for astigmatism can further comply with terms five and six and substantially reducing Zernike polynomials referring to astigmatism.
The inventive method further includes to calculate the wavefront aberrations resulting from an optical system comprising said modeled intraocular lens and cornea and expressing it in a linear combination of polynomials and to determine if the intraocular lens has provided sufficient reduction in wavefront aberrations. If the reduction in wavefront aberrations is found to be insufficient, the lens will be re-modeled until one or several of the polynomial terms are sufficiently reduced. Remodeling the lens means that at least one lens design parameter is changed. These include the anterior surface shape and central radius, the posterior surface shape and central radius, the thickness of the lens and its refractive index. Typically, such remodeling includes changing the shape of a lens surface so it deviates from being a spherical. There are several tools available in lens design that are useful to employ with the design method, such as OSLO version 5 see Program Reference, Chapter 4, Sinclair Optics 1996. The format of the Zernike polynomials associated with this application are listed in Table 1.
According to a preferred aspect of the first embodiment, the inventive method comprises expressing at least one corneal surface as a linear combination of Zernike polynomials and thereby determining the resulting corneal wavefront Zernike coefficients, i.e. the coefficient of each of the individual Zernike polynomials that is selected for consideration. The lens is then modeled so that an optical system comprising of said model lens and cornea provides a wavefront having a sufficient reduction of selected Zernike coefficients. The method can optionally be refined with the further steps of calculating the Zernike coefficients of the Zernike polynomials representing a wavefront resulting from an optical system comprising the modeled intraocular lens and cornea and determining if the lens has provided a sufficient reduction of the wavefront Zernike coefficients of the optical system of cornea and lens; and optionally re-modeling said lens until a sufficient reduction in said coefficients is obtained. Preferably, in this aspect the method considers Zernike polynomials up to the 4th order and aims to sufficiently reduce Zernike coefficients referring to spherical aberration and/or astigmatism terms. It is particularly preferable to sufficiently reduce the 11th Zernike coefficient of a wavefront front from an optical system comprising cornea and said modeled intraocular lens, so as to obtain an eye sufficiently free from spherical aberration. Alternatively, the design method can also include reducing higher order aberrations and thereby aiming to reduce Zernike coefficients of higher order aberration terms than the 4th order.
When designing lenses based on corneal characteristics from a selected population, preferably the corneal surfaces of each individual are expressed in Zernike polynomials describing the surface topography and therefrom the Zernike coefficients of the wavefront aberration are determined. From these results average Zernike wavefront aberration coefficients are calculated and employed in the design method, aiming at a sufficient reduction of selected such coefficients. In an alternative method according to the invention, average values of the Zernike polynomials describing the surface topography are instead calculated and employed in the design method. It is to be understood that the resulting lenses arriving from a design method based on average values from a large population have the purpose of substantially improving visual quality for all users. A lens having a total elimination of a wavefront aberration term based on an average value may consequently be less desirable and leave certain individuals with an inferior vision than with a conventional lens. For this reason, it can be suitable to reduce the selected Zernike coefficients only to certain degree of the average value.
According to another approach of the inventive design method, corneal characteristics of a selected population and the resulting linear combination of polynomials, e.g. Zernike polynomials, expressing each individual corneal aberration can be compared in terms of coefficient values. From this result, a suitable value of the coefficients is selected and employed in the inventive design method for a suitable lens. In a selected population having aberrations of the same sign such a coefficient value can typically be the lowest value within the selected population and the lens designed from this value would thereby provide improved visual quality for all individuals in the group compared to a conventional lens. One embodiment of the method comprises selecting a representative group of patients and collecting corneal topographic data for each subject in the group. The method comprises further transferring said data to terms representing the corneal surface shape of each subject for a preset aperture size representing the pupil diameter. Thereafter a mean value of at least one corneal surface shape term of said group is calculated, so as to obtain at least one mean corneal surface shape term. Alternatively or complementary a mean value of at least one to the cornea corresponding corneal wavefront aberration term can be calculated. The corneal wavefront aberration terms are obtained by transforming corresponding corneal surface shape terms using a raytrace procedure. From said at least one mean corneal surface shape term or from said at least one mean corneal wavefront aberration term an ophthalmic lens capable of reducing said at least one mean wavefront aberration term of the optical system comprising cornea and lens is designed.
In one preferred embodiment of the invention the method further comprises designing an average corneal model for the group of people from the calculated at least one mean corneal surface shape term or from the at least one mean corneal wavefront aberration term. It also comprises checking that the designed ophthalmic lens compensates correctly for the at least one mean aberration term. This is done by measuring these specific aberration terms of a wavefront having traveled through the model average cornea and the lens. The lens is redesigned if said at least one aberration term has not been sufficiently reduced in the measured wavefront.
Preferably one or more surface descriptive (asphericity describing) constants are calculated for the lens to be designed from the mean corneal surface shape term or from the mean corneal wavefront aberration terms for a predetermined radius. The spherical radius is determined by the refractive power of the lens.
The corneal surfaces are preferably characterized as mathematical models and the resulting aberrations of the corneal surfaces are calculated by employing the mathematical models and raytracing techniques. An expression of the corneal wavefront aberrations is thereby obtained, i.e. the wavefront aberrations of a wavefront having passed such a corneal surface. Dependent on the selected mathematical model different routes to calculate the corneal wavefront aberrations can be taken. Preferably, the corneal surfaces are characterized as mathematical models in terms of a conoid of rotation or in terms of polynomials or a combination thereof. More preferably, the corneal surfaces are characterized in terms of linear combinations of polynomials.
In one embodiment of the invention, the at least one nonspheric surface of the lens is designed such that the lens, in the context of the eye, provides to a passing wavefront at least one wavefront aberration term having substantially the same value but with opposite sign to a mean value of the same aberration term obtained from corneal measurements of a selected group of people, to which said patient is categorized. Hereby a wavefront arriving from the cornea of the patient""s eye obtains a reduction in said at least one aberration term provided by the cornea after passing said lens. The used expression xe2x80x98in the context of the eyexe2x80x99 can mean both in the real eye and in a model of an eye. In a specific embodiment of the invention, the wavefront obtains reduced aberration terms expressed in rotationally symmetric Zernike terms up to the fourth order. For this purpose, the surface of the ophthalmic lens is designed to reduce a positive spherical aberration term of a passing wavefront. The consequence of this is that if the cornea is a perfect lens and thus not will give rise to any wavefront aberration terms the ophthalmic lens will provide the optical system comprising the cornea and the ophthalmic lens with a negative wavefront spherical aberration term. In this text positive spherical aberration is defined such that a spherical surface with positive power produces positive spherical aberration. Preferably the lens is adapted to compensate for spherical aberration and more preferably it is adapted to compensate for at least one term of a Zernike polynomial representing the aberration of a wavefront, preferably at least the 11th Zernike term, see Table 1.
The selected groups of people could for example be a group of people belonging to a specific age interval, a group of people who will undergo a cataract surgical operation or a group of people who have undergone corneal surgery including but not limited to LASIK (laser in situ keratomileusis), RK (radial keratotomy) or PRK (photorefractive keratotomy). The group could also be a group of people who have a specific ocular disease or people who have a specific ocular optical defect.
The lens is also suitably provided with an optical power. This is done according to conventional methods for the specific need of optical correction of the eye. Preferably the refractive power of the lens is less than or equal to 30 diopters. An optical system considered when modeling the lens to compensate for aberrations typically includes the average cornea and said lens, but in the specific case it can also include other optical elements including the lenses of spectacles, or an artificial correction lens, such as a contact lens, a corneal inlay or an implantable correction lens depending on the individual situation.
In an especially preferred embodiment the ophthalmic lens is designed for people who will undergo a cataract surgery. In this case it is has been shown that the average cornea from such a population is represented by a prolate surface following the formula:   z  =                              (                      1            R                    )                ⁢                  r          2                            1        +                              1            -                                                            (                                      1                    R                                    )                                2                            ⁢                              (                                  cc                  +                  1                                )                            ⁢                              r                2                                                          +          adr      4        +          aer      6      
wherein,
(i) the conical constant cc has a value ranging between xe2x88x921 and 0
(ii) R is the central lens radius and
(iii) ad and ae are aspheric polynomial coefficients additional to the conical constant.
In these studies the conic constant of the prolate surface ranges between about xe2x88x920.05 for an aperture size (pupillary diameter) of 4 mm to about xe2x88x920.18 for an aperture size of 7 mm. Accordingly an ophthalmic lens suitable to improve visual quality by reducing at least spherical aberration for a cataract patient based on an average corneal value will have a prolate surface following the formula above. Since cornea generally produces a positive spherical aberration to a wavefront in the eye, an ophthalmic lens for implantation into the eye will have negative spherical aberration terms while following the mentioned prolate curve. As will discussed in more detail in the exemplifying part of the specification, it has been found that an intraocular lens that can correct for 100% of a mean spherical aberration has a conical constant (cc) with a value of less than 0 (representing a modified conoid surface), with an exact value dependent on the design pupillary diameter and the selected refractive power. For example, a 6 mm diameter aperture will provide a 22 diopter lens with conical constant value of about xe2x88x921.03. In this embodiment, the ophthalmic lens is designed to balance the spherical aberration of a cornea that has a Zernike polynomial coefficient representing spherical aberration of the wavefront aberration with a value in the interval from 0.000156 mm to 0.001948 mm for a 3 mm aperture radius, 0.000036 mm to 0.000448 mm for a 2 mm aperture radius, 0.0001039 mm to 0.0009359 mm for a 2,5 mm aperture radius and 0.000194 mm to 0.00365 mm for a 3,5 mm aperture radius using polynomials expressed in OSLO format. These values were calculated for a model cornea having a single surface with a refractive index of the cornea of 1.3375. It is possible to use optically equivalent model formats of the cornea without departing from the scope of the invention. For example multiple surface corneas or corneas with different refractive indices could be used. The lower values in the intervals are here equal to the measured average value for that specific aperture radius minus one standard deviation. The higher values are equal to the measured average value for each specific aperture radius plus three standard deviations. The used average values and standard deviations are shown in tables 8, 9, 10 and 11. The reason for selecting only minus one SD(=Standard Deviation) while selecting plus three SD is that in this embodiment it is convenient to only compensate for positive corneal spherical aberration and more than minus one SD added to the average value would give a negative corneal spherical aberration.
According to one embodiment of the invention the method further comprises the steps of measuring the at least one wavefront aberration term of one specific patient""s cornea and determining if the selected group corresponding to this patient is representative for this specific patient if this is the case the selected lens is implanted and if this is not the case a lens from another group is implanted or an individual lens for this patient is designed using this patients corneal description as a design cornea. These method steps are preferred since then patients with extreme aberration values of their cornea can be given special treatments.
According to another embodiment, the present invention is directed to the selection of an intraocular lens of refractive power, suitable for the desired optical correction that the patient needs, from a plurality of lenses having the same power but different aberrations. The selection method is similarly conducted to what has been described with the design method and involves the characterizing of at least one corneal surface with a mathematical model by means of which the aberrations of the corneal surface is calculated. The optical system of the selected lens and the corneal model is then evaluated so as to consider if sufficient reduction in aberrations is accomplished by calculating the aberrations of a wavefront arriving from such a system. If an insufficient correction is found a new lens is selected, having the same power, but different aberrations. The mathematical models employed herein are similar to those described above and the same characterization methods of the corneal surfaces can be employed.
Preferably, the aberrations determined in the selection are expressed as linear combinations of Zernike polynomials and the Zernike coefficients of the resulting optical system comprising the model cornea and the selected lens are calculated. From the coefficient values of the system, it can be determined if the intraocular lens has sufficiently balanced the corneal aberration terms, as described by the Zernike coefficients of the optical system. If no sufficient reduction of the desired individual coefficients are found these steps can be iteratively repeated by selecting a new lens of the same power but with different aberrations, until a lens capable of sufficiently reducing the aberrations of the optical system is found. Preferably at least 15 Zernike polynomials up to the 4th order are determined. If it is regarded as sufficient to correct for spherical aberration, only the spherical aberration terms of the Zernike polynomials for the optical system of cornea and intraocular lens are corrected. It is to be understood that the intraocular lens shall be selected so a selection of these terms become sufficiently small for the optical system comprising lens and cornea. In accordance with the present invention, the 11th Zernike coefficient, a11 can be substantially eliminated or brought sufficiently close to zero. This is a prerequisite to obtain an intraocular lens that sufficiently reduces the spherical aberration of the eye. The inventive method can be employed to correct for other types of aberrations than spherical aberration by considering other Zernike coefficients in an identical manner, for example those signifying astigmatism, coma and higher order aberrations. Also higher order aberrations can be corrected dependent on the number of Zernike polynomials elected to be a part of the modeling, in which case a lens can be selected capable of correcting for higher order aberrations than the 4th order.
According to one important aspect, the selection method involves selecting lenses from a kit of lenses having lenses with a range of power and a plurality of lenses within each power having different aberrations, in one example the lenses within each power have anterior surfaces with different aspherical components. If a first lens does not exhibit sufficient reduction in aberration, as expressed in suitable Zernike coefficients, then a new lens of the same power, but with a different surface (aspheric component) is selected. The selection method can if necessary be iteratively repeated until the best lens is found or the studied aberration terms are reduced below a significant borderline value. In practice, the Zernike terms obtained from the corneal examination will be directly obtained by the ophthalmic surgeon and by means of an algorithm they will be compared to known Zernike terms of the lenses in the kit. From this comparison the most suitable lens in the kit can be found and implanted. Alternatively, the method can be conducted before cataract surgery and data from the corneal estimation is sent to a lens manufacturer for production of an individually tailored lens.
The present invention further pertains to an intraocular lens having at least one nonspherical surface capable of transferring a wavefront having passed through the cornea of the eye into a substantially spherical wavefront with its center at the retina of the eye. Preferably, the wavefront is substantially spherical with respect to aberration terms expressed in rotationally symmetric Zernike terms up to the fourth order.
In accordance with an especially preferred embodiment, the invention relates to an intraocular lens, which has at least one surface, when expressed as a linear combination of Zernike polynomial terms using the normalized format, that has a negative 11th term of the fourth order with a Zernike coefficient a11 that can balance a positive such term of the cornea to obtain sufficient reduction of the spherical aberration of the eye after implantation. In one aspect of this embodiment, the Zernike coefficient a11 of the lens is determined so as to compensate for an average value resulting from a sufficient number of estimations of the Zernike coefficient a11 in several corneas. In another aspect, the Zernike coefficient a11 is determined to compensate for the individual corneal coefficient of one patient. The lens can accordingly be tailored for an individual with high precision.
The invention further relates to another method of providing a patient with an intraocular lens, which at least party compensates for the aberrations of the eye. This method comprises removing the natural lens from the eye. Surgically removing the impaired lens can be performed by using a conventional phacoemulsification method. The method further comprises measuring the aberrations of the aphakic eye, not comprising a lens, by using a wavefront sensor. Suitable methods for wavefront measurements are found in J. Opt. Soc. Am., 1994, Vol 11(7), pp. 1949-57 by Liang et. al. Furthermore, the method comprises selecting from a kit of lenses a lens that at least partly compensates for the measured aberrations and implanting said lens into the eye. The kit of lenses comprises lenses of different power and different aberrations and finding the most suitable lens can be performed in a manner as earlier discussed. Alternatively, an individually designed lens for the patient can be designed based on the wavefront analysis of the aphakic eye for subsequent implantation. This method is advantageous, since no topographical measurements of the cornea are and the whole cornea, including the front and back surfaces, is automatically considered.
The lenses according to the present invention can be manufactured with conventional methods. In one embodiment they are made from soft, resilient material, such as silicones or hydrogels. Examples of such materials suitable for foldable intraocular lenses are found in U.S. Pat. No. 5,444,106 or in U.S. Pat. No. 5,236,970. Manufacturing of nonspherical silicone lenses or other foldable lenses can be performed according to U.S. Pat. No. 6,007,747. Alternatively, the lenses according to the present invention can be made of a more rigid material, such as poly(methyl)methacrylate. The skilled person can readily identify alternative materials and manufacturing methods, which will be suitable to employ to produce the inventive aberration reducing lenses.